Bulk and boundary S-matrices for the SU(N) chain

Anastasia Doikou, Rafael I. Nepomechie

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We consider both closed and open integrable antiferromagnetic chains constructed with the SU(N)-invariant R-matrix. For the closed chain, we extend the analyses of Sutherland and Kulish - Reshetikhin by considering also complex "string" solutions of the Bethe ansatz equations. Such solutions are essential to describe general multiparticle excited states. We also explicitly determine the SU(N) quantum numbers of the states. In particular, the model has particle-like excitations in the fundamental representations [k] of SU(N), with k = 1,...,N - 1. We directly compute the complete two-particle S-matrices for the cases [1] ⊗ [1] and [1] ⊗ [N - 1]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU(l) × SU(N - l) × U(l), as well as a new "duality" symmetry which maps l ↔ N - l. With the help of these symmetries, we compute by means of the Bethe ansatz for particles of types [1] and [N - 1] the corresponding boundary S-matrices.

Original languageEnglish (US)
Pages (from-to)547-572
Number of pages26
JournalNuclear Physics B
Issue number3
StatePublished - Jul 22 1998
Externally publishedYes


  • Bethe ansatz
  • Boundary S-matrix
  • Boundary Yang-Baxter equation
  • Duality
  • Integrable spin chain
  • SU(N) R-matrix

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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